Temporal Memory-Aware Online Test-Time Adaptation on Dynamic Graphs

Test-time adaptation (TTA) on graphs aims to adapt a graph neural network (GNN) that is well-trained on the training graph to the test graph, which involves potential distribution shifts that may harm model generalization and test-time inference. While recent efforts have investigated TTA on static graphs, there is still a research gap on dynamic graphs learned with dynamic GNN (DGNN) models, where both structural connectivity and node semantics evolve continuously over time. This makes adapting a DGNN model for reliable test-time performance substantially challenging. To fill this gap, in this work, we propose a novel framework of temporal memory-aware Online Test-Time Adaptation on Dynamic Graphs, named DGOTTA, to effectively adapt well-trained DGNNs during test time. Specifically, the proposed DGOTTA contains three modules: (1) temporal-aware augmentation, to extend the diversity of test dynamic graphs for addressing complex temporal and spatial shifts; (2) memory-aware model prediction, to alleviate catastrophic forgetting; (3) consistency-guided online adaptation, to enforce temporal alignment and memory smoothness. Extensive experiments on three real-world datasets and four DGNN backbones demonstrate that DGOTTA significantly improves generalization under diverse distribution shifts and multiple model architectures.

When does distribution shift break graph neural networks calibration?

Graph neural networks (GNNs) are increasingly deployed in real-world applications where distribution shift is un-avoidable. However, how such shifts affect model calibration, defined as the agreement between predictive confidence and actual accuracy, remains poorly understood, and existing graph calibration methods typically rely on labeled validation data from the deployment distribution. In this work, I present the first closed-form theoretical characterization of GNN calibration under distribution shift. I show that calibration is governed by a single scalar quantity that explicitly depends on structural changes between the source and target graphs, as well as feature quality. This characterization precisely identifies when a model becomes over-confident, under-confident, or remains calibrated, and directly yields the optimal temperature scaling strategy. I further extend the analysis to graph convolutional networks with symmetric normalization, multi-class classification, and covariate shift, and derive a theoretical upper bound on the expected calibration error. My analysis also reveals that, under homogeneous distribution shift, a single global temperature is theoretically optimal, providing a principled explanation for why more complex node-wise recalibration methods offer no additional benefit. Building on these theoretical insights, I propose STAC, a source-free, label-free calibration method. Experiments on synthetic benchmarks demonstrate substantial calibration improvements, while evaluations on five real-world graph datasets show that reliable calibration without target labels remains challenging despite the strong predictive power of the theory.

Temporal Knowledge Graph Forecasting under Distribution Shifts: A Synthetic Evaluation

Temporal knowledge graphs (TKGs) represent evolving relational systems, whose underlying data-generating processes often change over time. Yet, TKG forecasting models are commonly evaluated only on empirical benchmark datasets that provide limited insight into the models' robustness to such distribution shifts. Recognising this issue, we study TKG forecasting under controlled shift environments using a synthetic TKG generator that encodes three temporal and structural properties -- recurrence, homophily, and periodicity -- as data-generating mechanisms. This allows us to evaluate seven forecasting architectures under stationary and shifting regimes. Our experiments suggest that robustness in TKG forecasting is highly signal-dependent. Recurrence-based and periodic regularities are largely recoverable under stationary conditions, and simple memory-based baselines can be competitive when recurrence dominates the data. However, structural breaks reveal limitations in model adaptivity, with shifts in latent entity-community structure posing the strongest challenge in our study. Overall, our findings improve the understanding of the capabilities and limitations of current TKG models confronted with temporal distribution shifts.

T3R: Deeper Test-Time Adaptation for Graph Neural Networks via Gradient Rotation

Graph Neural Networks (GNNs) deployed in real-world systems typically have fixed weights, often leading to degraded performance under distribution shifts. This issue can be mitigated by conventional fine-tuning, but in many real-world cases, collecting labeled data is expensive or infeasible. A potential approach is Test-Time Training (TTT), which adapts models' weights using unlabeled test data, yet it is typically limited to shallow updates that affect only a subset of model parameters. We propose T3R, leveraging multiple Rotograd matrices to improve task affinity between the target and auxiliary tasks, essential for effective test-time training. T3R further introduces a rotation technique that reorients self-supervised signals using these matrices to create surrogate gradients for the target task, allowing deeper adaptation across nearly the entire architecture. Empirically, T3R reduces MAE by 0.172 points over standard inference in regression datasets and achieves at least 9.37% relative improvement on cross-domain OGB classification benchmarks compared to models without adaptation. These results highlight the potential to develop an adaptation pipeline for graph-based systems, particularly in settings where conventional fine-tuning or retraining is infeasible.